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The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that…

Methodology · Statistics 2023-05-19 Andrew Herren , P. Richard Hahn

Weighting estimators based on propensity scores are widely used for causal estimation in a variety of contexts, such as observational studies, marginal structural models and interference. They enjoy appealing theoretical properties such as…

Methodology · Statistics 2021-10-06 Linbo Wang , Yuexia Zhang , Thomas S. Richardson , Xiao-Hua Zhou

In observational studies, the recorded treatment assignment is not purely random, but it is influenced by external factors such as patient characteristics, reimbursement policies, and existing guidelines. Therefore, the treatment effect can…

Methodology · Statistics 2024-09-02 Sara Poletto , Enrico Longato , Erica Tavazzi , Martina Vettoretti

Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and…

Methodology · Statistics 2025-04-11 Lars van der Laan , Ziming Lin , Marco Carone , Alex Luedtke

In this paper, we propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. We first use a class of penalized…

Methodology · Statistics 2018-12-21 Yang Ning , Sida Peng , Kosuke Imai

Understanding the dose-response relation between a continuous treatment and the outcome for an individual can greatly drive decision-making, particularly in areas like personalized drug dosing and personalized healthcare interventions.…

Machine Learning · Computer Science 2026-01-07 Jarne Verhaeghe , Jef Jonkers , Sofie Van Hoecke

We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work,…

Methodology · Statistics 2024-04-12 Yuhao Wang , Rajen D. Shah

Staggered treatment adoption arises in the evaluation of policy impact and implementation in many settings, including both randomized stepped-wedge trials and non-randomized quasi-experiments with panel data. In both settings, getting an…

Methodology · Statistics 2024-10-14 Lee Kennedy-Shaffer

Randomized controlled trials (RCTs) provide strong internal validity compared with observational studies. However, selection bias threatens the external validity of randomized trials. Thus, RCT results may not apply to either broad public…

Methodology · Statistics 2017-04-26 Ziyue Chen , Eloise Kaizar

Propensity score weighting approaches have been widely implemented in clinical research to estimate the effects of a treatment or exposure while mitigating the risk of confounding in the absence of random assignment. In practice, when…

Methodology · Statistics 2026-04-17 Emma K. Mackay , Amol A. Verma , Fahad Razak , Surain B. Roberts

This paper develops a unified framework for estimating continuous outcomes under multiple treatment levels in observational studies. We integrate the Generalized Propensity Score (GPS), Covariate Balancing Propensity Score (CBPS), and…

Methodology · Statistics 2025-09-22 Byeonghee Lee , Joonsung Kang

Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world…

Statistics Theory · Mathematics 2026-04-14 Shuyuan Chen , Peng Zhang , Yifan Cui

We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…

Statistics Theory · Mathematics 2018-10-09 Linh Tran , Maya Petersen , Joshua Schwab , Mark J van der Laan

Propensity score (PS) methods have been increasingly used in recent years when assessing treatment effects in nonrandomized studies. In terms of statistical methods, a number of new PS weighting methods were developed, and it was shown that…

Methodology · Statistics 2022-12-20 Tim Filla , Holger Schwender , Oliver Kuß

In observational surveys, post-stratification is used to reduce bias resulting from differences between the survey population and the population under investigation. However, this can lead to inflated post-stratification weights and,…

Applications · Statistics 2016-06-24 Yannick Vandendijck , Christel Faes , Niel Hens

We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance…

Methodology · Statistics 2022-09-27 Hanzhong Liu , Fuyi Tu , Wei Ma

Exposure measurement error is a ubiquitous but often overlooked challenge in causal inference with observational data. Existing methods accounting for exposure measurement error largely rely on restrictive parametric assumptions, while…

The propensity score is widely used for causal inference in observational studies, but common parametric estimators can produce biased and inefficient effect estimates when model assumptions are violated. Nonparametric approaches reduce…

Methodology · Statistics 2026-04-09 Maosen Peng , Yan Li , Chong Wu , Liang Li

Precision medicine aims to tailor treatment decisions according to patients' characteristics. G-estimation and dynamic weighted ordinary least squares (dWOLS) are double robust statistical methods that can be used to identify optimal…

Methodology · Statistics 2021-11-10 Denis Talbot , Erica EM Moodie , Caroline Diorio

In this article, we propose the outcome-adjusted balance measure to perform model selection for the generalized propensity score (GPS), which serves as an essential component in estimation of the pairwise average treatment effects (ATEs) in…

Methodology · Statistics 2021-07-28 Honghe Zhao , Shu Yang